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Fitting In

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ

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Look Before You Leap

Can you spot a cunning way to work out the missing length?

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Triangle Midpoints

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Figure of Eight

Age 14 to 16 Challenge Level:

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement so that one pair of opposite sides cross and the other pair are parallel.

Figure of eight on a pegboard

How many different "figure of 8" arrangements can be made ?

Which of these arrangements has the area of the lower (green) portion nearest to double the area of the upper (yellow) portion ?

For printable sets of circle templates for use with this activity, please see Printable Resources page.